Trilateration is the process of locating an unknown point by using its distances from reference points of known
position. If the unknown point is 
, the reference points are 
, and the measured distances are 
, then 
satisfies
 |
for 
,
..., 
.
Geometrically, each equation constrains 
to a circle in the plane or a sphere in three-dimensional space, and the desired position
lies in their common intersection.
In the plane, distances to three reference points that are not collinear generically determine a unique point. In space, four reference points that are not coplanar are generically required. With noisy measurements, the equations generally have no exact common solution and are instead fit approximately, for example by least squares fitting (Cotera et al. 2016). Trilateration uses measured distances, whereas triangulation in surveying uses measured angles.
